The discussion revolves around the output of a Mathematica plot involving Jacobi elliptic functions, specifically examining the expression involving \( k^2 \) and whether it yields a constant value of 1 across a specified range of \( t \). Participants explore the behavior of the functions and their expected properties based on mathematical theorems.
Participants express differing views on the expected output of the plots, with some confirming oscillation and others suggesting constant values under different conditions. The discussion remains unresolved regarding the implications of the addition theorems and the correct parameters to use.
There is a potential misunderstanding regarding the parameters \( k \) and \( m \) in the Jacobi functions, which may affect the interpretation of the results. The discussion also highlights the dependence on specific versions of Mathematica, which could influence the output.
k = 2;
Plot[k^2 JacobiSN[t, k]^2 + JacobiDN[t, k]^2, {t, 0, 10}]Yes, that oscillates between 1 and 2 (Mathematica 12.0.0.0).joshmccraney said:Can anyone confirm if the following in Mathematica gives an output that is not 1? I'm getting some sort of sinusoid, but I should get 1.
Code:k = 2; Plot[k^2 JacobiSN[t, k]^2 + JacobiDN[t, k]^2, {t, 0, 10}]
Thanks!
But the addition theorems here https://en.wikipedia.org/wiki/Jacobi_elliptic_functions imply ##k^2 sn^2 + dn^2 = 1##? Am I missing something?DrClaude said:Yes, that oscillates between 1 and 2 (Mathematica 12.0.0.0).
Plot[2 JacobiSN[t, k]^2 + JacobiDN[t, k]^2, {t, 0, 10}]Do you mean ##k^2## instead of 4?Bill Simpson said:I don't know if this helps, but
Code:Plot[2 JacobiSN[t, k]^2 + JacobiDN[t, k]^2, {t, 0, 10}]
does appear to be 1 for all values of t while 4 JacobiSN[t, k]^2 + JacobiDN[t, k]^2 is not.
I noticed that by plotting the two functions separately and guessing the needed scale factor.